S5000 tells us the series, but not the model, so we won't know exactly what sort of hardware you are working with. That said, HP Slimlines in that series and pretty much all others are not made with games in mind, especially not games like GW2. They tend to have weak processors and no or very weak dedicated graphics cards. If you can get the exact model we can tell you a bit more, but ultimately you may need an entirely new system to play the game.

The exact model and/or some tech details such as cpu, video type and power supply wattage, would definitely help.
But, even without that info, I can guess that your main problem is the lack of a good video card. Unfortunately, being a "slimline" model, it can probably only take low-profile cards which limits your upgrade options to an HD6670 or HD7750 - if the power supply is powerful enough.